Question

If the 4th and 9th terms of a G.P are 54 and 13122 respectively then find the G.P

Answer 1

Heya dear !

The general formula for the nth term of a geometric progression is: 
a(n) = ar^(n-1) 

a : first term 
r : common ratio 

So, the terms of a geometric progression are: 
a, ar, ar², ar^3, ar^4, etc. 

Fourth term: 
ar^3 = 54 

Ninth term: 
ar^8 = 13122 

Dividing the 9th term by the 4th term: 
ar^8 / ar^3 = 13122 / 54 
r^5 = 243 
r = 243^(1/5) 
r = 3 

Now we just need to figure the first term: 
ar^3 = 54 

Plug in r=3: 
a(3^3) = 54 
27a = 54 
a = 54/27 
a = 2 

Answer: 
a(n) = 2*3^(n-1) 

2, 6, 18, 54, 162, 486, etc.

Hope this helps (:

Answer 2

Answer:

THE G.P. IS 2,6,18,54...............